Polio can and does mutate almost instantly around the vaccines, but since some of the vaccines are live polio anyway people don't really care. "Mutation" is not really a word that matters, what matters is if a variant is causing problems.
On rare occasions the live vaccine actually reverts. Polio is an amazing story because the live vaccination campaign may have had collateral impact on the families of the vaccinated as they shed particles.
Rare? It's in almost everyone who gets the vaccine. I don't have a direct citation, but I don't think it's generally doubted, though it's not something that's easy to do a direct controlled test on.